On Strong Edge Metric Dimension of Crystal Cubic Carbon Structure
Keywords:
Strong edge resolving set, Crystal structure of cubic carbon, Strong edge metric dimensionAbstract
The strong edge metric dimension of a carbon-based crystal structure is examined in this paper using the framework of chemical graph theory. The goal is to identify the smallest edge-resolving set that uniquely identifies each pair of edges based on their distance relationships. The crystal structures are treated as connected graphs. Exact formulations for the strong edge metric dimension of these carbon-based graph families are found by taking use of their underlying structural features. The results gained show how network topology affects edge distinguishability and offer closed-form mathematical characterizations for the graph classes under consideration. These results support the structural and mathematical analysis of crystalline materials based on carbon and advance the theoretical development of graph invariants in chemical graph theory.
Downloads
References
Trinajsti´c N Chemical Graph Theory CRC Press (1983)
Slater P J 1975 Leaves of trees Congr. Numer. 14 549-559
Chartrand G, Eroh L, Johnson M A and Oellermann O R 2000 Resolvability in graphs and the metric dimension of a graph Discrete Appl. Math. 105 99–113
Melter R A and Tomescu I 1984 Metric bases in digital geometry Comput. Gr. Image Process 25 113–21
Seb˜o A and Tannier E 2004 On metric generators of graphs Math. Oper. Res. 29(2) 383–93
Khuller S, Raghavachari B and Rosenfeld A 1996 Landmarks in graphs, Disc. Appl. Math. 70 217–29
Al-Qudah Y, Jaradat A, Sharma S K and Bhat V K 2024 Mathematical analysis of the structure of one-heptagonal carbon nanocone in terms of its basis and dimension Phys. Scr 99 055252. DOI 10.1088/1402-4896/ad3add
Okamoto F, Crosse L, Phinezy B, and Zhang P 2010 The local metric dimension of a graph Math. Bohem. 135 239–55
Kelenc A, Kuziak D, Taranenko A and Yero I G 2017 Mixed metric dimension of graphs Appl. Math. Comput. 314 420–38
Kelenc A, Tratnik N and Yero I G 2018 Uniquely identifying the edges of a graph: the edge metric dimension Discret. Appl. Math. 251 204-20
Hernando M C, Mora M, Slater P J and Wood D R 2008 Fault-tolerant metric dimension of graphs Convexity Discrete Struct. 5 81–5
Liu X, Ahsan M, Zahid Z and Ren S 2021 Fault-tolerant edge metric dimension of certain families of graphs AIMS Math. 6 1140-52
Chartrand G and Zhang P 2006 The theory and applications of resolvability in graphs: A survey. In: Proceedings of the 34th Southeastern International Conference on Combinatorics, Graph Theory and Computing Congr. Numer. 160 47–68
Raza H, Hayat S and Pan X F 2019 On the fault-tolerant metric dimension of certain interconnection networks J. Appl. Math. Comput. 60 517–35
Somasundari M and Raj F S 2019 Fault-tolerant resolvability of oxide interconnections Int. J. Innov. Tech. Explor. Eng. 8 1-15
Krishnan S and Rajan B 2016 Fault-tolerant resolvability of certain crystal structures Appl. Math. 7 599-604
Sharma S and Bhat V K 2022 Fault-tolerant metric dimension of zero-divisor graphs of commutative rings AKCE Int. J. Graphs Comb. 19 24-30
Sharma S K and Bhat V K 2022 Fault-tolerant metric dimension of two-fold heptagonal-nonagonal circular ladder, Discrete Math. Algorithms Appl. 2150132 https://doi.org/10.1142/S1793830921501329.
Ahmad A, Asim M A and Baˇca M A R T I N 2024 Fault-tolerant metric dimension of barycentric subdivision of Cayley graphs. Kragujevac J. Math 48 433-39
Prabhu S, Manimozhi V, Davoodi A and Guirao J L G 2024 Fault-tolerant basis of generalized fat trees and perfect binary tree derived architectures J. Supercomput. https://doi.org/10.1007/s11227024-06053-5
Raza H, Hayat S and Pan X F 2018 On the fault-tolerant metric dimension of convex polytopes Appl. Math. Comput. 339 172–85
Liu J B, Munir M, Ali I, Hussain Z and Ahmed A Fault tolerant metric dimension of wheel related graphs, Hal Archives Hal-1857316v2 https://hal.archives-ouvertes.fr/hal01857316v2/document
Mojgan A, Strong Edge Metric Dimension of Graphs. Available at SSRN: https://ssrn.com/abstract=4769772 or http://dx.doi.org/10.2139/ssrn.4769772
Raza H, Hayat S, Imran M and Pan X F 2019 Fault-tolerant resolvability and extremal structures of graphs Mathematics 7 78–97
Azhar K, Zafar S, Kashif A, Aljaedi A and Albalawi U 2022 The Application of Fault-Tolerant Partition Resolvability in Cycle-Related Graphs Appl. Sci. 12(19) 9558 https://doi.org/10.3390/app12199558
Gao W, Siddiqui M K, Naeem M and Rehman N A 2017 Topological characterization of carbon graphite and crystal cubic carbon structures Molecules 22 1496 https://doi.org/10.3390/molecules22091496
Baig A Q, Imran M, Khalid W and Naeem M 2017 Molecular description of carbon graphite and crystal cubic carbon structures Can. J. Chem. 95 674-86
Imran M, Naeem M, Baig A Q, Siddiqui M K, Zahid M A and Gao W 2019 Modified eccentric descriptors of crystal cubic carbon J. Discret. Math. Sci. Cryptogr. 22(7) 1215-28
Yang H, Naeem M, Baig A Q, Shaker V and Siddiqui S K, Vertex Szeged index of crystal cubic carbon structure J. Discret. Math. Sci. Cryptogr. 22 1177-87
Zhang X and Naeem M 2021 Metric dimension of crystal cubic carbon structure J. Math. 3438611 https://doi.org/10.1155/2021/3438611
Sattar A and Javaid M 2022 Topological characterizations of crystal cubic carbon structures Can. J. Chem. 100 828-39
Yang H, Siddiqui M K, Naeem M and Rehman N A 2020 Molecular properties of carbon crystal cubic structures, Open Chem., 18 339-46
Zahid M A, Naeem M, Baig A Q and Ggao W 2018 General fifth M-Zagreb indices and fifth M-Zagreb polynomials of crystal cubic carbon Util. Math. 109. https://utilitasmathematica.com/index.php/Index/article/view/1284
Yang H, Siddiqui M K, Arshad M and Naeem M 2018 Degree-distance based topological indices of crystal cubic carbon structure Atoms 6 62 https://doi.org/10.3390/atoms6040062
Sharma S, Bhat V K and Lal S 2023 Multiplicative Topological Indices of the Crystal Cubic Carbon Structure Cryst. Res. Technol. 58 2200222 https://doi.org/10.1002/crat.202200222
Sharma S, Bhat V K and Lal S 2023 Edge resolvability of crystal cubic carbon structure Theor. Chem. Acc. 142 24 https://doi.org/10.1007/s00214-023-02964-3
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All papers should be submitted electronically. All submitted manuscripts must be original work that is not under submission at another journal or under consideration for publication in another form, such as a monograph or chapter of a book. Authors of submitted papers are obligated not to submit their paper for publication elsewhere until an editorial decision is rendered on their submission. Further, authors of accepted papers are prohibited from publishing the results in other publications that appear before the paper is published in the Journal unless they receive approval for doing so from the Editor-In-Chief.
IJISAE open access articles are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. This license lets the audience to give appropriate credit, provide a link to the license, and indicate if changes were made and if they remix, transform, or build upon the material, they must distribute contributions under the same license as the original.
